The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2  1  0  1  X  1  1  1 X^2+X  1  1  1 X^2  X  1 X^2  1  X  1  0  1  1  1  1 X^2+X  1 X^2+X X^2  1  1  1 X^2+X  X X^2+X  X  1  1  1  1  1  X
 0  1  1  0 X^2+X+1  1 X+1 X^2+X  1 X^2  1 X^2+X+1 X^2+X+1  0  1  X  1 X^2+1  1 X^2+1 X^2+X  0  1 X^2+1 X^2+X X^2  1  1 X+1  1 X^2+X+1  1  X  1 X+1  X X^2+1 X^2+1  1  1  1  1 X+1 X+1 X^2+1  1  1  1  1  0  0 X+1  1 X+1 X^2
 0  0  X  0 X^2+X  0 X^2 X^2  X X^2+X X^2+X  0  X  X  0 X^2 X^2+X  0 X^2+X  X X^2+X  X X^2  0 X^2+X  X X^2+X  X X^2+X X^2+X X^2 X^2 X^2  0 X^2+X  X X^2 X^2+X X^2+X X^2 X^2 X^2 X^2+X X^2 X^2  X  X X^2+X  X X^2 X^2  X  X X^2+X  X
 0  0  0  X  0  0  0 X^2 X^2 X^2 X^2  X  X  X  X  X  X  X X^2+X  X X^2+X X^2+X X^2+X  0 X^2  0  X  0  X  X X^2+X X^2+X  0  0  X  0  X X^2  X X^2+X X^2  X  0 X^2  0  X  0  0 X^2 X^2 X^2+X  0  0 X^2+X X^2
 0  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0  0

generates a code of length 55 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+55x^48+110x^49+316x^50+180x^51+575x^52+184x^53+613x^54+168x^55+607x^56+144x^57+533x^58+118x^59+273x^60+52x^61+71x^62+30x^63+20x^64+18x^65+3x^66+14x^67+4x^68+4x^69+2x^71+1x^80

The gray image is a linear code over GF(2) with n=220, k=12 and d=96.
This code was found by Heurico 1.16 in 0.75 seconds.